Question: Divide the following complex numbers: $\dfrac{12 e^{5\pi i / 4}}{3 e^{\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $12 e^{5\pi i / 4}$ ) has angle $\frac{5}{4}\pi$ and radius 12. The second number ( $3 e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius 3. The radius of the result will be $\frac{12}{3}$ , which is 4. The angle of the result is $\frac{5}{4}\pi - \frac{1}{3}\pi = \frac{11}{12}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{11}{12}\pi$.